Company LOGO Edit your slogan here DKT 122/3 DIGITAL SYSTEM 1 WEEK #8 FUNCTIONS OF COMBINATIONAL LOGIC (ENCODER & DECODER, MUX & DEMUX)

Company LOGO Topic Outlines  Encoder  Decoder  Multiplexers (MUX)  Demultiplexers (DEMUX)

Company LOGO Topic Outlines  Encoder  Decoder  Multiplexers (MUX) Multiplexers (MUX)  Demultiplexers (DEMUX)

Company LOGO Encoder  Encoder converts information such as decimal number, alphabetical character, or symbols into some coded form, such as BCD or binary  Encoder is usually used for:  Data representation  Data security

Company LOGO Question 1: Design a Decimal to BCD Encoder Hints: (a)Draw a Truth-Table showing input and output - How many inputs? : 10 (0 to 9) - How many outputs? : 4 because we need 4 bits to express 9 (1001) (b) From the Truth-Table, get the equation for each output - How many Boolean expression? : 4 since there are 4 outputs (c) Based on the output equation, draw a circuit for basic decimal-to-BCD encoder Encoder

Company LOGO Draw a Truth-Table showing input and output DECIMAL DIGIT BCD CODE A3A3 A2A2 A1A1 A0A Encoder

Company LOGO (b) From the Truth-Table, get the equation for each output: A 3 = Σ m(8, 9) A 2 = Σ m(4, 5, 6, 7) A 1 = Σ m(2, 3, 6, 7) A 0 = Σ m(1, 3, 5, 7, 9) (c) Based on the output equation, draw a circuit for basic decimal-to-BCD encoder (a) Logic symbol for a 10-line-to 4 line encoder (b) Logic diagram. A 0-digit input is not needed because the BCD outputs are all low when there are no HIGH inputs (a) (b) Encoder

Company LOGO  A decoder is a circuit that creates an output based on the binary states of a given input  Do the opposite of encoder Decoder Decoder block diagram

Company LOGO Basic Binary Decoder Example:  To determine when a binary 1001 occurs on the input of a digital circuit, AND gate can be used as the basic decoding element.  AND gate -> produce HIGH output when all inputs are HIGH  How to ensure that inputs to the AND gate are HIGH when binary 1001 occurs? Other than this input combinations, the output is 0 Decoder

Company LOGO Question 2: (a)Determine the logic required to decode the binary by producing a high level (active-HIGH) on the output. Active-HIGH  produce HIGH output Decoding function, A4A4 A2A2 A1A1 A0A0 A3A3 Decoder

Company LOGO 4-bit Decoder  This type of decoder is called 4-line-to-16-line decoder or 1-of-16 decoder  For a 4-bit decoder, there are 16 possible combinations (2 4 =16). This means that 16 decoding gates are required Decoder

Company LOGO 3 to 8 Binary Decoder Question : Is this active-HIGH or active-LOW output? Decoder

Company LOGO Example: Seven Segment Decoder A seven segment decoder has 4-bit BCD input and the seven segment display code as its output: In minimizing the circuits for the segment outputs all non- decimal input combinations (1010, 1011, 1100,1101, 1110, 1111) are taken as don’t-cares D C B A a b c d e f g don’t care inputs -- Decoder

Company LOGO Multiplexers (MUX)  MUX is a device that allows digital information from several sources to be routed onto a single line for transmission  It is made up of several data- input lines and a single output line. It also has data-select inputs which permits digital data on any one of the inputs to be switched to the output line.  MUX is also known as data selectors Logic symbol for a 4-input multiplexer (4:1 MUX) n select inputs 1 data output 2 n data inputs

Company LOGO 2:1 MUX Logic circuit Truth-table Multiplexers (MUX)

Company LOGO DATA-SELECT INPUTS INPUT SELECTED S0S0 S1S1 00D0D0 01D1D1 10D2D2 11D3D3 If a binary 0 (S 0 =0 and S 1 =0) is applied to the data-select lines, the data on input D 0 appear on the data-output line 2 data-select lines means that any one of the 4 data-input lines can be selected 4-to-1 MUX S0S0 Z D1D1 D0D0 S1S1 D3D3 D2D2 D0D0 D1D1 D2D2 D3D3 S1S1 S0S0 Z 4:1 MUX Multiplexers (MUX)

Company LOGO Total expression for the data output is: Logic diagram for 4:1 MUX 4:1 MUX Multiplexers (MUX)

Company LOGO Question 3: Construct an 8:1 multiplexer using block diagram. 8 input lines means there must be 3 data select lines. Multiplexers (MUX)

Company LOGO Demultiplexers (DEMUX)  DEMUX reverse the multiplexing functions  It takes digital information from one line and distributes it to a given number of output lines  DEMUX is also known as data distributor 1-line to 4-line DEMUX 1 data input n select inputs 2 n data outputs

Company LOGO 1:4 DEMUX Demultiplexers (DEMUX)

Company LOGO Question 4: Construct a 1:4 DEMUX using block diagram. Show the equivalent Truth-Table. 1-4 DEMUX S 0 I 0 Q 1 Q 0 S 1 Q 3 Q S 0 I 0 Q 1 Q 0 S 1 Q 3 Q 2 S0S0 S1S1 Q0 Q1 I 0 Q2 Q3 S1S0I1Q3Q2Q1Q Truth-table Block diagram Logic circuit Demultiplexers (DEMUX) END